Despite his second-term battles with the national GOP, Mayor Bloomberg is set to introduce a pro-gun-rights Republican congressman at a Manhattan breakfast next week.

He’ll help bring Rochester Rep. Tom Reynolds up on stage at a breakfast held by the Association for a Better New York. Reynolds is leading the effort to elect GOP House members across the nation.

Word of the plan has raised eyebrows since Bloomberg launched his second term with a crusade against illegal guns and lawmakers who kowtow to the gun lobby.

“Mayor Bloomberg has said again and again that no two people are going to see eye to eye on all issues,” the mayor’s press secretary, Stu Loeser, said yesterday. “But New Yorkers should back . . . lawmakers who back us. Reynolds has been an extraordinary supporter of New York City.”

L.D. Platt, a spokesman for Reynolds, who helped secure billions in federal aid for the Big Apple after 9/11, agreed.

“We can have differences of opinion,” he said. “That is what makes the Republican party [run].”